Find the HCF of the numbers in each of the following using the prime factorization method 504, 980

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Consider 36, 756, and 1001. Find the prime power factorization of each. Use the prime power factorization (make it clear you are using the prime factorization) to find the gcd of each pair of these numbers. Use the prime power factorization (make it clear you are using the prime factorization) to find the lcm of each pair of these numbers.

Question 3 Factors and Multiples Exercise 2D

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Answer:

To get the HCF using the division method. The remainder becomes the new divisor, while the old divisor becomes the new dividend. We repeat the process until there is no more remainder. The HCF of all three numbers is the new divisor.

The prime factors of 504 =2^{3\ }\times\ 3^2\ \times7

The prime factors of 980 =2^2\times\ 5\times\ 7^2

∴ HCF =2^2\ \times\ 7 = 28

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Find the HCF of the numbers in each of the following, using the prime factorization method:
504, 980

The given numbers are 504 and 980.
We have:

504 = 2 × 2 ×2 × 3 × 3 × 7 = 23 × 32 × 7
980 = 2 × 2 × 5× 7 × 7 = 22 × 5 × 72
∴ HCF of the given numbers = 22 × 7 = 28

Concept: Highest Common Factor

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Page 2

Find the HCF of the numbers in each of the following, using the prime factorization method:
72, 108, 180

The given numbers are 72, 108 and 180
We have:

Now, 72=2 × 2 × 2 × 3 × 3 = 23 × 32
108 = 2 × 2 × 3 × 3 × 3 = 22 × 33
180 = 2 × 2 × 3 ×3 × 5 = 22 × 32 × 5
∴ HCF =22×32 =36

Concept: Highest Common Factor

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Page 3

Find the HCF of the numbers in each of the following, using the prime factorization method:
84, 120, 138

The given numbers are 84, 120, and 138.
We have:

Now, 84 = 2 × 2 ×3 × 7120 = 2 × 2× 2 ×3 × 5138 = 2 × 3 × 23

∴ HCF = 2 × 3 = 6

Concept: Highest Common Factor

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Page 4

Find the HCF of the numbers in each of the following, using the prime factorization method:
106, 159, 371

The given numbers are 106, 159, and 371.
We have:

Now, 106 = 2 × 53159 = 3 × 53371 = 7 × 53

∴ HCF = 53

Concept: Highest Common Factor

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Page 5

Find the HCF of the numbers in each of the following, using the prime factorization method:
272, 425

Given numbers are 272 and 425.
We have:

Now, 272 = 2 × 2× 2 × 2 × 17425 = 5 × 5 × 17

∴ The required HCF is 17.

Concept: Highest Common Factor

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Page 6

Find the HCF of the numbers in each of the following, using the prime factorization method:
144, 252, 630

The given numbers are 144, 252, and 630.
We have:

Now, 144 = 2 × 2× 2 × 2× 3 × 3252 = 2 ×2 × 3× 3 × 7630 = 2 ×3 × 3× 5 × 7

∴ HCF = 2 × 3 × 3 =18

Concept: Highest Common Factor

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Page 7

Find the HCF of the numbers in each of the following, using the prime factorization method:
1197, 5320, 4389

The given numbers are 1197, 5320, and 4389.
We have:

Now, 1197 = 3 × 3× 7× 19 = 32 × 7 × 19
5320 = 2 × 2 × 2× 5 × 7 × 19 = 23 × 5 × 7 × 194389 = 3 ×7 × 19 × 11

∴ Required HCF = 19 × 7 = 133

Concept: Highest Common Factor

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Page 8

Find the HCF of the numbers in each of the following, using the division method:
58, 70

We have:

∴ The HCF of 58 and 70 is 2.

Concept: Highest Common Factor

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Page 9

Find the HCF of the numbers in each of the following, using the division method:
399, 437

The given numbers are 399 and 437.
We have:

∴ The HCF is 19.

Concept: Highest Common Factor

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Page 10

Find the HCF of the numbers in each of the following, using the division method:
1045, 1520

The given numbers are 1045 and 1520.
We have:

∴ The HCF of 1045 and 1520 is 95.

Concept: Highest Common Factor

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Page 11

Find the HCF of the numbers in each of the following, using the division method:
1965, 2096

The given numbers are 1965 and 2096.
We have:

∴ The HCF is 131.

Concept: Highest Common Factor

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Page 12

Find the HCF of the numbers in each of the following, using the division method:
2241, 2324

The given numbers are 2241and 2341.
We have:

∴ HCF = 83

Concept: Highest Common Factor

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Page 13

The given numbers are 658, 940, and 1128.
First, we will find the HCF of 658 and 940.

Thus, the HCF of 658 and 940 is 94.
Now, we will find the HCF of 94 and 1128.

Thus, the HCF of 94 and 1128 is 94.
∴ The HCF of 658, 940, and 1128 is 94.

Page 14

Find the HCF of the numbers in each of the following, using the division method:
754, 1508, 1972

The given numbers are 754, 1508, and 1972. First, we will find the HCF of 754 and 1508.

So, the HCF of 754 and 1508 is 754.Now, we will find the HCF of 754 and 1972.

So, the HCF of 754 and 1972 is 58.
∴ The HCF of 754, 1058 and 1972 is 58.

Concept: Highest Common Factor

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Page 15

The given numbers are 391, 425, and 527.First, we will find the HCF of 391 and 425.

So, the HCF of 391 and 425 is 17.Now, we will find the HCF of 17 and 527.

So, the HCF of 17 and 527 is 17.
∴ The HCF of 391, 425, and 527 is 17.

Page 16

The given numbers are 1794, 2346, and 4761.First, we will find the HCF of 1794 and 2346.

So, the HCF of 1794 and 2346 is 138.Now, we will find the HCF of 138 and 4761.

So, the HCF of 138 and 4761 is 69.
∴ The HCF of 1794, 2346, and 4761 is 69.